Abstract
The present paper studies global hypoellipticity and global solvability on the two dimensional torus T{sup 2} for a class of second order differential operators with variable coefficients of the type P=(D{sub x}-ia(x)D{sub y}) (D{sub x}-ib(x)D{sub y})+(a`(x)-b`(x))D{sub y}+c(x). Necessary and/or sufficient conditions for global solvability and global hypoellipticity are proposed. In particular if Rea(x) {identical_to} 0 and/or Reb(x) {identical_to} 0 Siegel type conditions on the diophantine approximation of the averages {integral}{sub 0}{sup 2{pi}}Rea(x)dx or/and {integral}{sub 0}{sup 2{pi}}Reb(x)dx occur. We also indicate some results for more general class of operators and for the n-dimensional torus T{sup n}, n > 2. (author). 18 refs.
Gramchev, T;
[1]
Popivanov, P;
[2]
Yoshino, M
[3]
- International Centre for Theoretical Physics, Trieste (Italy)
- Bylgarska Akademiya na Naukite, Sofia (Bulgaria). Matematischeski Inst.
- Chuo Univ., Tokyo (Japan)
Citation Formats
Gramchev, T, Popivanov, P, and Yoshino, M.
Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients.
IAEA: N. p.,
1991.
Web.
Gramchev, T, Popivanov, P, & Yoshino, M.
Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients.
IAEA.
Gramchev, T, Popivanov, P, and Yoshino, M.
1991.
"Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients."
IAEA.
@misc{etde_10113318,
title = {Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients}
author = {Gramchev, T, Popivanov, P, and Yoshino, M}
abstractNote = {The present paper studies global hypoellipticity and global solvability on the two dimensional torus T{sup 2} for a class of second order differential operators with variable coefficients of the type P=(D{sub x}-ia(x)D{sub y}) (D{sub x}-ib(x)D{sub y})+(a`(x)-b`(x))D{sub y}+c(x). Necessary and/or sufficient conditions for global solvability and global hypoellipticity are proposed. In particular if Rea(x) {identical_to} 0 and/or Reb(x) {identical_to} 0 Siegel type conditions on the diophantine approximation of the averages {integral}{sub 0}{sup 2{pi}}Rea(x)dx or/and {integral}{sub 0}{sup 2{pi}}Reb(x)dx occur. We also indicate some results for more general class of operators and for the n-dimensional torus T{sup n}, n > 2. (author). 18 refs.}
place = {IAEA}
year = {1991}
month = {Jul}
}
title = {Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients}
author = {Gramchev, T, Popivanov, P, and Yoshino, M}
abstractNote = {The present paper studies global hypoellipticity and global solvability on the two dimensional torus T{sup 2} for a class of second order differential operators with variable coefficients of the type P=(D{sub x}-ia(x)D{sub y}) (D{sub x}-ib(x)D{sub y})+(a`(x)-b`(x))D{sub y}+c(x). Necessary and/or sufficient conditions for global solvability and global hypoellipticity are proposed. In particular if Rea(x) {identical_to} 0 and/or Reb(x) {identical_to} 0 Siegel type conditions on the diophantine approximation of the averages {integral}{sub 0}{sup 2{pi}}Rea(x)dx or/and {integral}{sub 0}{sup 2{pi}}Reb(x)dx occur. We also indicate some results for more general class of operators and for the n-dimensional torus T{sup n}, n > 2. (author). 18 refs.}
place = {IAEA}
year = {1991}
month = {Jul}
}